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Dictionary Construction for Patch-to-Tensor Embedding

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Part of the Lecture Notes in Computer Science book series (LNISA,volume 7619)

Abstract

The incorporation of matrix relation, which can encompass multidimensional similarities between local neighborhoods of points in the manifold, can improve kernel based data analysis. However, the utilization of multidimensional similarities results in a larger kernel and hence the computational cost of the corresponding spectral decomposition increases dramatically. In this paper, we propose dictionary construction to approximate the kernel in this case and its respected embedding. The proposed dictionary construction is demonstrated on a relevant example of a super kernel that is based on the utilization of the diffusion maps kernel together with linear-projection operators between tangent spaces of the manifold.

Keywords

  • Image Segmentation
  • Tangent Space
  • Spectral Decomposition
  • Ambient Space
  • Recursive Little Square

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2012 Springer-Verlag Berlin Heidelberg

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Salhov, M., Wolf, G., Bermanis, A., Averbuch, A., Neittaanmäki, P. (2012). Dictionary Construction for Patch-to-Tensor Embedding. In: Hollmén, J., Klawonn, F., Tucker, A. (eds) Advances in Intelligent Data Analysis XI. IDA 2012. Lecture Notes in Computer Science, vol 7619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34156-4_32

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  • DOI: https://doi.org/10.1007/978-3-642-34156-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34155-7

  • Online ISBN: 978-3-642-34156-4

  • eBook Packages: Computer ScienceComputer Science (R0)